Question: Simplify the following expression: $r = \dfrac{-5p^2 + 45p + 50}{p - 10} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ r =\dfrac{-5(p^2 - 9p - 10)}{p - 10} $ Then we factor the remaining polynomial: $p^2 {-9}p {-10} $ ${-10} + {1} = {-9}$ ${-10} \times {1} = {-10}$ $ (p {-10}) (p + {1}) $ This gives us a factored expression: $\dfrac{-5(p {-10}) (p + {1})}{p - 10}$ We can divide the numerator and denominator by $(p + 10)$ on condition that $p \neq 10$ Therefore $r = -5(p + 1); p \neq 10$